{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e3cce145",
   "metadata": {},
   "source": [
    "# 项目6. RLC振荡电路\n",
    "\n",
    "- 姓名：杜东洋\n",
    "- 学号：20201050438\n",
    "- 邮箱：Starry_339@163.com"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
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    "image-3.png": {
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"
    },
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"
    }
   },
   "cell_type": "markdown",
   "id": "26468630",
   "metadata": {},
   "source": [
    "## 项目介绍\n",
    "\n",
    "RLC电路是一种由电阻R、电感L、电容C组成的电路结构。RLC电路的组成结构一般有两种：串联型，并联型。作用有电子谐波振荡器、带通或带阻滤波器,本次项目主要是研究串联型RLC电路的振荡情况.\n",
    "\n",
    "我们知道:在如图电路中,当R(电阻)、L(电感)、C(电容)的量值不同时，特征根可能出现以下三种情况，对应于三种不同的阻尼情况。\n",
    "\n",
    "(1) R>2(L/C)^0.5时，S1、S2为不相等的实数根，为非振荡放电过程，为过阻尼情况。\n",
    "\n",
    "(2) R=2(L/C)^0.5时，S1、S2为两个相等的实数根，此时为临界阻尼情况。\n",
    "\n",
    "(3) R<2(L/C)^0.5时，S1、S2为共轭复数根，为振荡放电过程，为欠阻尼情况。\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "![image-2.png](attachment:image-2.png)\n",
    "\n",
    "![image-3.png](attachment:image-3.png)\n",
    "\n",
    "\n",
    "## 项目目的\n",
    "本项目需要结合我们学习过的数值微分和数值积分(梯形法,辛普森法,高斯积分法等等)来选定区间由已知数据点进行积分和微分的拟合."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d2a27d1",
   "metadata": {},
   "source": [
    "## 1.准备RLC数据(参数)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a86aa3d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "## 电阻R阻值为0.1欧姆,电感L为0.1H,电容C为1微法,电源电动势取12V.\n",
    "R = 0.1\n",
    "L = 0.1\n",
    "C = 1e-6\n",
    "E = 12\n",
    "d = (4*L/C - R**2)**(1/2)\n",
    "c1 = d/(2*L)\n",
    "c2 = -R/(2*L)\n",
    "c3 = 2*E/d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d5c43265",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 导入必要的库函数\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "eaffd0ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.arange(0,6,0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a2d2fc6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def j(p):\n",
    "    return 2*E*np.sin(d*p/(2*L))*np.exp(-R*p/(2*L))*(1/d)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2426c0ca",
   "metadata": {},
   "source": [
    "## 2.作图展示电流的变化情况"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "31906070",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d68f273f70>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,j(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6809b6ac",
   "metadata": {},
   "source": [
    "## 3.解析微分和解析积分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "09b019d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "## 给出电流的导数\n",
    "def di(t):\n",
    "    return 2*E*(1/d)*(c1*np.cos(c1*t)*np.exp(c2*t) + c2*np.sin(c1*t)*np.exp(c2*t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "22fa7e27",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d68fa2c1f0>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,di(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "383e2ed7",
   "metadata": {},
   "outputs": [],
   "source": [
    "## 给出电流的不定积分\n",
    "def si(t):\n",
    "    return c3*(np.exp(c2*t))*(-c1*np.cos(c1*t)+c2*np.sin(c1*t))/(c1**2+c2**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "35136653",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d68fa98430>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SFX6xjFDde0eDXmQlRNtU8IM+af8/oYt7R0Sc1PUjmXch+Ik8OsJ+RAI+DHaEXQv+T45PGl8/dnLK1VqCIJaXlhD8Qrmxy6b6e6eN24Lu/4sB6ED1pq1EW6ZSOw8X0DZu0xK2TP14REATfJm1ALCQrfXw20N+JHPySZ3TqYIxPH2gI4RJl4L/ylgSAZ8H67oieP78vKu1BEEsLy0h+IYHbxKtUP28FQWTlk4h+DKVdr5URqguiz8a9EqtTZt4+LGgV37TNltCJOA19h/aQz6kXFT4c5mi0b/fGQkgVVBcZfGcmExjS28MOwbacG4mI72OIIjlp6UEv6HC93prnreioKg1HTpApWNHNl65vsIPB3xyHr4+PKWtzsOXFfyFXKlm/6A97EdBUaWD32YyBXRHtQq/K6r9HJHPL8PpyRS29cewsTeKC7MZ6UjoaiaTeVf5/wRBmNMagl+2EHzJCr+oqDUdOkDthq8TeZMbRtjvkRJd8y4d+U3bRL3g69aQmMLlxFymaBzYike0f4vOHyeUsoqJZB5DnRFs7omhVOau2zo//8Q53PLXj+JLT513tY4giEZaQvBLilYd1nfpVDx8e+EtKGqDpcMYQ9DncezSKascRUVtsHTCkvHK5h6+ZunIVL0L2ZLRkgloFT4AqY1bpawikS0Zlo4QftlohqlUASoH1sTDWNsZBlDp65flK89cAAB84cnzrtYRBNFISwh+0WrTVr8BOOXhFErlhrWAVuU7VfiipbPR0vFKndI1PPxAbYWvckhNvUrkioiHA8b37SFN8GUq/Dnduuk2KnxtbULS0hnTxX1NPISBjhAAzZ6R5dJcFudmMhjuCuPiXBbTKXezfAmCqKUlBF+IckNapvDhJbp06it8QG4IihDl+rbMkORM3HReQdjvNaKVgUqLpoyts5ArGUNTgMpcXZlefBHL0BGpr/DlLJ0xvaNnTTyMgXZN8N20dYrRjL9yy3oAwOGRhPRagiAaaQnBt960ddOl03gwS2YIev3wE4GspZMpKjV2DuAubTNbKCMWXJylkxQbxvr7d+rCL7tpO6VX8/1tIUSDPrSFfK4q/JN6UJvI8Tkx6T7H52vPXsRPT1D/P0EALSb49VW69MErk01XAAj5vI4Ts4SoN1g6fllLp4xooL6lU67C55wjU1SMdE6gYunI9OKLny82ekN+L8J+L+YlPfyZdBF+LzM+YQy0hzDhosI/PZXGQLtmB/XEgrjgcgD7U6dn8CcPvowPfvF5XJqjWb4E0RqCvyxdOiYevt/j6KMLwa//hBAOaJaO08ZrrqggHKit8GNBufC1fEmFyivpnEBlJq5ML754TVuo8gmhM+LHvGSXzmxaa+kUB9a6ogFXWfwj8zms64oAADZ0R3Bhzl0f//ePTBhfP3J0wuaVBNEatITgi4NCZjNtAbmTtqaWjosKP+Rv9PBV7vzeuVIZkfpTukaevn2VLiZqxaoqfLEfIGPpiI3d6liHzmhA2tKZSRfQ01bZMO6OBYyNYBnGEjmsiWve/7ruCC7Muqzwz8zgNdt7sbk3iqfPXNFwVoJYlbSE4BvhaUvy8M02bWUqfO35sImHDwB5h2iGbLFR8GU3bcXM3OoKnzGmB6hJWDp1Hj6g+fjygl80Dm2JtbIVflnlmFjIG+2cazrCmEzmpQ9u5YplnJ3JYPdwHNet7cCx8aTUumoOXUrgHx895Sp7iCBWMy0l+FYVvlOVXig1Dk8B3Fb4jZYO4By+liuWG9bKTr2qxDLUrm8P+6UtHcZqW0I7owFpD382XTB6+AGtvTORLUqJ9lQqD0XlWBPXBL+/PQiVA7MZudbMM9NpcA5s62/DzsF2jC3kpdtJAe0MwkceeBF/96OT+P9+cFx6HUGsZlpC8AuWaZkuohUsKnynHn67Lp3q5+3WN1T4AckKX7d0InV7AG0hn9GBY0cyryAW8MFT1RLqxsNP5EpGZw+gefgql5vHO5PSxLmvTbN0evV/TyXlBP+k3tGzrT+Grf0xAMBZF1k+L11K4PxsFkGfBw++MOoqP4ggVistIfjCJ68Xbb9XEzIpS8ckLz/o8yLvWOGbWzohyRGJ2WK50Q4KyK0VWT3VsQyAZgmlJQQ/XVBq7BxAy9VP5kuOU8KKiopssWzk8APapwNA7qSu8PpFfk9fu2YNTaXkunwuzmXBGDDcFcFQp7bx6ybW4akzs2AM+LO37EKmWMaR0QXptYKpZF46xpogrgStIfgWlg5jDAGfx/bgFefcsktHpsK32rSVtXTyJsFrAZ8Hfi9zDF/LWFg6saBf6tBWKl+q6dABNDuIczjO1F2oy+EHYPj5MoIvbCPxCaG/3V2Ff2kuh/62EII+L9bqttCIC8E/PJLAlt4Y7tGndB284C7a+anTM7j9//0J3vXppx1tP4K4UrSE4JfKKnweVmNNCIJej22Fr+jjEU3bMn0yJ231tkyrTVub9ZxzZE0sHUCzaXIOopsxiWUAtK4dOcFvPPQl+vgXHGwdQ/BrKnzt6zkJH17cFMTp3t6YdrOYlBT8kfkshrs0oY8GfeiM+DEyL9/lc3Y6gy19MfS1hdATCxinfmX55M9Oo1TmODqWxE+PT7taSxCXi5YQ/KJivukKaNWyneAbA8xN2zKdT9oaB6+sPHybKr1U5iirvGEtAEQCXscKP2tl6YTk0jbNLB3Zk7oLdcPTgeoK39nDn88W4WGVG0zA50FnxC9t6YzM54zKHgDWdoalg9tKZRUX57LY1BsFAGwfaHN1yjeVL+GZs3P4rVdvRk8sgO8fGZdeK5jPFHFqESeLCcKOlhH8+qRMgaPgl8yD1wCtai8oqu3hqXxJhYdV9gsE4YD28+wsHXEzqD94BWiC7+ThC1FvbOuUtXQUE0tHZPFIWjpLqPA7I4GaT2V9bSFMSQSocc4xnSqgXw9sA4CheETa0rkwm4Wicmzq0TZ7t/a14fRUWjqT/8D5eZRVjju39ODWTd044HLSV7ao4B2fegr3/M/H8e8vjrpaSxB2tIbgl+0rfLsqvWARy1D9mN36XEnbdK0ejwjIzcTNljRRNa/wfcbBKsv1RQVeD2u49raQD0VFdfSWU/lSzaEroCLgTp02ZoIf9HkRC/qkK3yxySvoaw8a+Tx2JPMKimXVsIEArcIfmc9KifbZ6TQAYHOfJvjDXRFki2XpMwSHRhJgDNg9HMdN6zsxmsi5ipT4zqExYzrY3//oJA1/IZaNlhB8MZPWjICDh28IvlmWji7EdoKfLzX20QNyHr6o4M09fK9h2ViR0XN46m82IpvHKZohlVeMHB2BkcXjYOmIISnxSK1oa/EKchV+V91a2Qp/Jq29pqdK8Ic6w8iXVCnRFu2bwtIZ1g9/XZL8hHBsPIkN3VFEgz7sGmwHAByfkD/49d3D49jUE8XfvuM6XJzL4rjL/YMz02l8+Gsv4DuHxlytI5qflhB8qy4bQBNyu3iDooOHD8B2CErOSvAlWiuzhqVjJfjOm7b1/j0AxHTRtju4pX0CUBs8fNF14xSvLCr8+htGZzSAOYk+/vlMybCABL1tQcykC44V70yqUfDFAa6xhHOlfW46g55Y0Li5revW2jplA9iOT6Swc7ANALBF/5RweiottbaoqDhwfh53bu3Ba3f2AQAePym/6cs5x0ceeBHfOzyOjzzwIs5My70v0Rq0jOBbWjqOFb4IP1tchV8oqQ0tmQCMCVi2Hr7Fhi8ARII+xwrfLJYBqEQz2A1BESdx6y2dWMAHxpwFP5EtoS3og6/uk1U87Jc6eDWXrYxWFHRHAyiVueOhsZm0VsVX5/j0tWniP512FvyxhRyGOisbvsN6H/8liS4fpaxiZD6HjT3ap4PuWBCdET/OTMsd+jo+kUSuVMa+jd3oawthXVcEL15MSK0FtANjR0aT+IN7tsHrYfjasxel1wLaDePbL4zgcz8/S+2kTUhLCH7JwcNfSpcOYG/LWFk6Hg9DyO+R2rQ1tXT8XiMrx4pMUWkQbEAui0c8V79p6/EwtAWdT+omcyWjo6eaeMSPBYeIA8455vVN22pETIOTLTOtd/JUV/i9QvAlLKGJhTz62ytro0EfuqIBXJpztnQmUwWUVW4c9gK0Kv+MZIV/fFyzb8QnhBvXxfHSpYTUWgD46YlpeBjwgds24K6tvfjRK5Ou9gC+e3gcH/3GIfy37x3D3//wpPQ64uqgJQS/WLbr0vHaHrwSB6usRhwCzpu2ZoIPOGfiiwrebH006JOydOpjFYDKfNx0wbrSTpkEpwk6Is5V+kLd8HRBPOxHwmFtMq9AUXlDhS++n03bi/ZMWmvprL5hCPGXEfzJZN6Y0CUY1jd9nRjRbZ/qltAtfTGclrRWjk+kEPJ7sL5b+4Swc7AdE8m847kHwYHzc9i1ph0dYT9evb0XF+eyrlJGP/WzM9je34b79qzBvzx13nVw3FOnZ/DbXz2IR49NulpHXBlaQ/CXtGkrY+nYV/hmlgzgLPjik4NZhR+W3bQNWls6aZtPCOJ/9PqDV4C2ceto6eRqh6cLOiIBLOTsoxnqT9kKhGjPOlT4M+kCuqLBmrGQIb8X7SGfo+DnimUk8wr66gR/qCsi5eGLXv9qS2hzbwxzmaLUhvGJySS29bcZ176tX6v0xfQvO0plFS9eTGDv+i4AwE36vw9JjoY8NZnCK+NJvO+Wdfi12zagoKj44VF54Z5YyOM3vnwAD788gQ995eCi9g8yBYXiKC4jrSP4Vpu2Po+tYNt16VQsHbsuHXMPHwBCAfu5tlnD0mkU3WjAC0XltjerbNGiwheCb2PLiOfaQyaiLeHD21X4nNvvH1RydKwqfGfB74kFGh7vbQti2uHTgRjBWF/hD3WGMZbIO2YIiV7/NfFawQeAczPOAnhiIoXtusgDMILfZE76Hh3T/P+bN2hCv60/hpDfg0OX5HKAfnZC2xy+Z1c/9gzH0RML4IlT8hvGX332AvKlMh787dvg93rw6Z+dkV4LAI+dnMZN/+1HuOWvH8WB83Ou1hJytITgF5Zw0tauS0e2wjcLXgOc59qKSsfsE4I4jGX3CSFdKFt06SzN0mkP+aXaMk0FX6/6Ezlr0Z7P2Au+U1vndLpoePbV9LYFHSt8Ifj9dYK/piOMYll1HOAyOp9Db1uwxoYb7hJdPvZ7ANOpAmbSRWwfqAj+2ngY0YBX6tTtixe1A143re8EAPi8Hly7pkO6wn/m7Cw290axJh4GYwz7N/fgqTOzUnsAnHN89/A49m/uxg3rOvGW69fg4ZfHpcZ4Atrf4z/65iEMdoTRHvLjo984BMVFQinnHF988hw+8IXn8KNXyE6yoiUE3+7gVdBx09ba0hFVv32F72DpOGz4AuZtmUYvvc3H32xRaZiHC2gbvozZWzpWXTqAdtrW7qQt5xzJXKkmOE1gCL6NJ12foyMI+bWDWzNOFX6qULNhK+htCzkK/oQh+LXrB/RTu04HqEYS2Rr/HqjYOxcdLCFx4GtrVYXPGMPWfrloh1NTaXSE/TXXfv1QHEfHFqTE88jYAnYPxY3vb9vcjalUQarD6JXxJM7NZPDm69cAAN68exCZYhnPnJWbNPadQ2OYTBbwV2+/Fn/x1mtwcS6LH7gYS/nNgyP4y++8gufPzeFDXzmIw5I3OcFUKo//8cgJ/O9nLkgP2bkaaQnBL5VVBO2iFew2bW1P2kpU+Iq1pRN2iEfIFsvweZjpzUrcBKx8fFXlWlumiWB7PAzRgH1EslWXDuBs6eRLKopl1bTC7whrIm43NUs8V3/SFtDHJNp44Zxza0sn5lzhizTO6lgGABjUvx9zyOMZna9t6QS0G1V/e9BR8MXm6obuSM3j2/pjODXpbAednkpja1+s5qDd7uEO5EsqTjl0CU2nCphMFrBrTbvx2P5N3QCApyVE+yfHpgAAv6Cni968oQtBnwePS1pCDx0aw6beKPZv6sbdO/ow0B7CQy/JHRwrKir++yMncOO6OJ7547vRGQngvz9yQmotoP1df/dnnsEnfnoa/+Xfj+AvHjoqvRbQ/l/71sER/O33jxs37dVKSwj+kvrwbbp0hJDbRSTnimWj575xvRc5u7U2nw5EAqbVBldW/3QQM9m01R73OVo6QZ/H9PduD/mRK5Ut/9yEXRMPN4quqPDtbhhzmRICXo/pp5PuaMB26lW6oKCgqBYVfhCZYtn2wNlEMo+w34u2uhulUeHbRDuoKsdYojKWsZp1XRFnwZ/LwOdhDZ8QNvfGMJspOnbqnJ5KGwe9BDslT/oeHdN8/mvXdhiPre+OoCcWMKwiOw5enMe2/hi69T/3kN+LfRu78MSpGce1+VIZz52fw2u294ExLdX23msH8LOT01KZTz84OoGpVAEfed02dET8+MD+9fj5qRlp8f3iE+dwbiaDr/3mLfhPt2/E/37mgqs47L9++Bj+4N8O4dOPncF9n3jSdejdT09M4be/ehB/98MTl33DumUEf9HhaYalYz4ABbDuw+ecI6805tkLnDz8nEkWviDiUOFnjeC0xgof0Hx8u2iFZL4xKVNgnLa18PHNcnQEYiCKnaUznymiM+pviIQAgK5o0HbT1jh0ZSL44vDVjM3G7WQyj4GOUMN790SD8HsZxm0snel0AcWyWtODLxiW6PI5P5vFUGe44bDaJn3T94zNpu9suoC5TLFB8Df2RBHweoz+fiuOjmk3hOoKnzGGPcPO5wBUleOFC/PG3oHgzq09ODWVdrTBDl6YR1FRcfuWbuOxN18/iKKiSrV3/uDIOHrbgrhzSw8A4D37huGTPHSWzJfwzz8/i9ft7Mdtm3vwh6/fhs6IH595TG7D+cD5OXzuiXN4/63r8cTHXoOAz4OPfeuw9NmH7x0exwe/+DyeOzeHT/z0NH7zywcuq6XUMoJvt2mrqNyy+6KgqGAmaZdAVYVvccMollVwbt5HD8j14VsKftC+wq9Mu7Ku8FMOB6/M7BygKk/HokoXYm5u6Uh4+NnGQ1eCnljAti3TyNGx2LQF7HvxJ5N548ZQjcfD0N8ewriNpSP69Ifi5hX+RDJva/9dmM0Y/ffViEyfczZeuohuqBd8v9eDrf0xHHPo8jk6toD13ZGGrqw9w3Gcnc7Yfro4PZ1GMq8YbaCC/Zs0AX72nL0l9MTpGfg8DPs2VgT/xnWd6IoGjM4hKwpKGY+fnMHrdvYZyap9bSG8ensfHn553FF4Hz48jmRewYdfsxmAViC975Z1+NGxSVyUOL/wmcfPojsawJ+8cSeGOiP4w9dvxwsXE/ihxMZxvlTGX37nKHYPdeCJj70Wf/P26/Dk6Vl88clzjmsXy7IIPmPsXsbYCcbYacbYx02eZ4yxf9CfP8wYu3E53lcWp7RM8RozxDxbs2qzUuGbr80XtcctBd+hLdPO0nGq8K2Gnwi0MYd2lk7JusI3MvHNbxiiwjfrw/d5PWgL+hy7dOo3bAVd+hB1qxt0JUfHvC0TcBL8QkOHjmCwI2Rb4YuWzHoPH9DiGTi3HrPIOceF2WyDfy/Wej0MZ20q/NMmG76CHQPtOD5ub+kcGU3imqrqXnDDOq1qf8lmE1TYH/UV/s7BNkQDXsd46KdOz+CGdfGaBgGPh+GurT14/OS0bSvss2fnkC4oeN3O/prHX39NP8YW8njZYTTlgy+OYlNvFHuG48Zj7791AzyM4evP239CGE3k8OixSbxn37BRmL3rpiFs6oniH39yyvFm8/XnLmIqVcDH3rADIb8X7755GHfv6MPf/fCk7afQpbBkwWeMeQF8EsAbAOwC8F7G2K66l70BwFb9n/sBfGqp7yuLqnKUytz24BVg7cNrwWvmouv1MPi9zLJqE/NuLfvwJbp0HC0dC1umMt7QWvDtLJ1U3jyWAahk4lv58HaWDqCf1HWq8C0EvzsWhKJySztJ/I/Sa+HhA7DsxeecG5aOGYMdYVsPXwi+qYevC7mVjz+fLSGVV0wr/IDPg3VdEZy1qfBPTaYRCXixxuTadw62YSpVsDyhnMyXcHEui2vWdDQ8d/1QBxgDXrLJ8zlwfh7d0UDDzcrn9eDG9Z143qanfiFbwuHRBdy2uafhuVdv78NspogjY9ai/eNjkwj5Pbh9S+361+3sh9fD8IhNp89oIodnz83hbXvW1hR0Ax0hvGpbLx58YdTWXvm6bhm9d9864zGf14PfuHMTjowm8dw56987Xyrj04+dwb6NXcbmOGMMf/KmnSgoZXzK5RkGWZajwt8H4DTn/CznvAjgAQD31b3mPgBf5hrPAIgzxgaX4b0dKanWm65AZfRgoWwufgWlbJm0CWhVvpWlY8yztbhhhP1eFBXV8i+VVfgZUPHmLTdtbXJ4AOepV2kbD9/J0hGPm2XpAFrlbxevMG8SjSzoFoevLGyd6XQRjDW2dALayV2vh1lW+Au5EgqKamrpAJUK36pyG03k0BUNmO6brDN68c0F//ysJubrTSp8ANjUEzUy8s04M61t2Jp9Et0xoFXuVoe3XtH9e7MKvy3kx5beGF66ZF2lv3BR8+/N3nvfhi6cmExZ3uCfPjsDzoE7tjYK/p1be8AYLG0dzjkePTaFO7b0NnyK7owGcMvGLvzgiLXgiy6gt+1Z2/DcL944hIlkHk+dMd90LioqHnj+Il67o79hz+YdN65FZ8SPzz1hbc386/OXMJks4Pfu3lrz57a5N4Z33DiEB18cdRyfuhiWQ/DXArhU9f2I/pjb1wAAGGP3M8YOMMYOTE8vfRZo0aatEoDRrmm1cVsoWdtB4uda/YfJ2fTRa4/bh6/lis6WjtWYQ9Gfb1Wlx4I+o9feDLMB5gKnISgLuRIYQ0OniyAeDiBh0ZZZVjkSuZJNhW9/2nY6VUBnJNCw8Qlon8i6owFLwRfzcq0q/IGOEIqKdaZ+/VjFanpjQQR9HstMfeEXWwp+ryb4VvbGqck0tvTGTJ/boQexvWJh6xzRbQ+zCh8AbtAD3MxudHOZIs7NZAzrp56bN3aBc+DABfNq98nTs4gGvDWWiqA7FsT1azvwmEU89LHxFEYTOdyzq8/0+ddfM4Az0xmctoil+I+XRnHjurjx6auau3f2oSPsxzcPjpiu/f6Rccyki3j//vUNz4X8Xrz/1vX48bFJ05u0qOBv3tCJ/Zu7G57/o3u340e/f5elFbwUlkPwG2/rQP3fDJnXaA9y/lnO+V7O+d7e3t4lX5wQckcP30rwbbL0Ae0/rnWFLzx8iz58h6lXuVLZdLwhoN1oPMz6pK2wdMz68AHRlqlYVqspuwrfYa5tMqdFI5sNjQc0S8eqwk9ki+Ac6DLx/wHn07Yz6YKpnSPobQtaDlGZsDhlKxjs0MTcyscfnc+a+veA5kkPdYYtNwIvzGbBGEw7fABgY08MBUU1ncubypcwkcxjS7+54PfEguiJBS0HqbwylkR/e9D0dDIA7BnuxHy2ZBrCdkjv4LlxXdxibRx+L8NzFrbOk6dnsG9jl2UX3au29eLFi/OmBcKPj02CMeC1O/pNVgL3XjsAxoDvHW6s8k9NpnB8IoW37l5jujbk9+ItuwfxyNEJ07/nX3nmAtZ3R4zOoHp+Zf96+D0e0w3Ybzx/CRPJPD5y9zbTT0V9bSGjvXW5WQ7BHwEwXPX9EID6ExMyr7ksiM1Yu7bM6tfVo1k61nda2wq/aG/pGGMOLURbq/DNr5sx7fCU1Ulb4c+b9bIDmqWjcvMNZ1XlSBcVywo95Pci4PPYVvhmp2wF8bC1h2936AqotFtanbadSRdqcvDrsYtXMGIV2qw3bQFzweecYzRhXeED9r34F+YyGGgPWVZ1RqeOScUoOnS29jVu2Ap2DrZZ9uIfGVvAtRbVPQCj+jZrz3zx4jy8HobrhszXh/xeXLe2w3TjdiyRw9mZTIP/Xs2rtvdB5VonTz2PHpvE7qG45Y2qvz2Em9d34XsvN0rNdw6Pw8OAN15v7Sy/86Zh5EsqHj5cO4T+2HgSz5+fx6/cst6yqOlrC+Gte9bg3w6M1PxdLyhl/NPPzmDv+s6aNtQrxXII/vMAtjLGNjLGAgDeA+Chutc8BOADerfOrQAWOOfj9T/ocmBU+A6btrYVvoXoApVB5mYYm7aWlo59H3+uVLbsoxfrrW4Wwtu3Wi82c1Mmh68yRQWcm5+yFWiJmeY3m2ReMQ1dEwgP39wi0K7HqktHtGta2SraKVvr6qjPTvB1Ie9rt/bwAWBiobHKns0UkS+plhU+oAn+pTnzuboXZ7OGz2+GEHyzw0RWLZnV7Bxsx8nJdEPEQq5YxumptKl/L9jWH0Mk4DUX/EsJbO9vs/17evPGLhweSTT8PX9SF3Ez/16we6gDHWF/g48/mczj0MgC7tllXt0L3nT9IE5OpmsOQ3HO8Z1DY9i/WRsyY/feW/pi+Lc6W+fzT5xD0OfBO28asn3vX79jI3KlMr7y7AXjsS8+eR7jC3n83uvMq/vLzZIFn3OuAPgdAI8AOAbgG5zzo4yxDzHGPqS/7GEAZwGcBvDPAH57qe8ri6ylYyXaTpZO0GYIekFi0xawsXSK1ln6gCbaVh5+ulBGwGt+Uhao+Otm8Qp2wWmC9rDP9uCVVYcOoHn4ZZWbbhrPWUQjCwI+D9pDPsuOk5lU0VbwxZhEMy98MpVHPOK3/DPviQXh85gfvqp06FiL9nBXBKmCYnoG4fxsFhtMOnSM644F0Rb0GfN2qzk9lUbA5zFm75qxY6ANRUU1NocFxyeSUDlwzVrrCt/n9eC6tR0NJ25VleOlSwncYGHnCPZt6EKpzBtuGE+cnkFPLFCTDmr23nds7cFjJ6drbpQ/1g9k1bdj1vMG3db5blWV/tKlBM7NZPCW683tHAFjDO/dtw4HL8zj6TPaWYJLc1k8+OIo3nfLOstPoYKdg+24e0cfPvGT0zg9lcaF2Qz+4dFTuGdXv+1N7nKyLH34nPOHOefbOOebOed/pT/2ac75p/WvOef8w/rz13HODyzH+8ogrBq78DTAycNfpKUjBN/JwzcRbaWs5dFYbdqK9TnLLh0FEYtDV0BlM9esNVMIsVkWvqAjbJ2Jn8yVbCv8DpsANWHpdJv00Qu6Y0HTLp1MQUGuVLYXfL2t0yzLZzJZaIhFrsY4fGUi+KM2PfgCIzWzbpBKpqBgJl0w3TwUMMawsde8U+f0VBqbeqKmG9UC0alzrO7E7VGbDp1q9qyL45XxZM3f9bMzaaTyiumGazUin//5qjbFssrx2Mlp3Lm117HSffW2XkynCjWbzv/+4ig290axzWLfQtDXHsLtm3vw9ecuGtf+2cfPoi3kw5ts7BzBL9+yDgPtIfzN94+hqKj4m+8fg5cx3H/XJse1APDX77gO4YAX7/7M03j7Pz2FgM+DP3tzfdf6laPpT9ouedO2VLbt0pHZtLXq0hFWj1mFLx6zaqsEtFO0Vr30mULZ8tCVttba0hHdO86WzmIrfOsuH6cKH9DzdEw8fOOUrc3NQgw2Mdu4nUzmGwaf1KO1ZjZaOuKUrVkPvkBYNvU+vvjeqkNHsKknatqLf8okQ6eezX1R+Dyswcc/OraAeMRvu/cAADcMd6JU5jWi+4Lem2/VoSPoiPixY6Ctxod/4eI8EtkS7t5p3mFTzau2ac0bj+jDWM7PZPD8+Xn84k1DUrbIh1+zBVOpAr727EUcn0jiB0cn8P5b19v+/RaE/F786Zt24vDIAm79m0fx8MsT+P17thkb+E70t4fwlV+/BdcPdeCG4TgeuP9W48a/ElgrQpNgtGU6bNpaxiPIWDoWFb5MH37166oxPh3YCH444LPcOM0UFMtYBaBi15hZOkkJS6cj7MeFWfO+8GS+ZBzOMiOui7lphZ8pIhLw2lpZXdGAaceIXayCoPq07c66Am8ymceOAWt7AQAG42G8bHLqdDSRQ3vIZ/vJZthC8MXvsr7L2tIBtEydf39prCZjKVNQcGk+i1+80d5PDvq82Nwba6jwX7q0gOvWdjgKp7BtXrqYwI26wD+pWzKbeuyvGwB+4ZoB/ONPTmEymUd/ewg/PjYJn4fhrm3OnXh97dpBqAeeu4jfetVmfOWZC/Aw4B032P/Ogv2bu3HHlh787fePIxbyoTsawK/fsVFqLQC8ZfcalFWOhw6N4VXbevEBk1ZMO3ataccXP7jP1ZrLRfNX+KJLx8nSsY1WsBYfuwq/Yum49/BFLEPEzsMPeI2QtHoyFtOuBIalY2IJiZuAVZcOIDz8xrUFpYx8yTwaWWA3BMUuR0egWTqNFfp0Svt5tm2ZFrNtlbKK6ZR1rILA6vDVyHzO1r8HtD9zbRh6fYWv3TjtLB2gsnFb7cMfn0iBc2dLBtD68asjFpL5Ek5MJBsiEczobw9hsCOEF3UfXlgyd23rtexUqeatu9eAc81LL6sc3z2kDUuxu0FW89uv3oypVAH/6V+ex5efvoC33zBkeV7CjP/1nj2455p+bO9vw798cJ/rtse33bAWX/i1m/Grt21Ykc3W5aJlKnzrLh39pK1FlV5QyvZdOjYevrB0rD4hiCotV2y8YWRLSs1rrNZbpmUWzefZCqJSm7Y2Przu4XPOa/4HEJ07MpaOVYVv1aEj6I5qmfiqymvEpmLpOFf49ZbObKYIlcPR0hloD6GgqJjPlmquc3Q+5yjYgEjNrLWELsxmEY/4bf/MAC35EgDOTmeM2GNhseyUEfyBdvzHS2NYyGptsy9eTEDlFY/diRvWxY2N20MjCSSyJbxmu7MlA2gdRNeubcdXnrmASMCL0UQO//ebdkqtBYBbNnXjd1+7BZ/46WnsGmzHf3mz/FpAKxI++b4rGuG1Kmn+Ct/Bwxdi7hSeZoVdhV8oabEMVhVQyKbCFxu5doIfDfis0zILiq2HL+was8TMiodvU+GH/FD0ISvVLDjEKgDVm7ZmFb71KVtBdywAlaPh8JYQfLsN32jQh2jA21Dhiwhfu01bAFgTF734FdHmnGNkvnHSlRlmvfjnZsxTMuvZ1BODh6Fm+tUrY0l0hP2mGTr1iOjjw6MJAMDB83PwMG1DVobbNvdgZD6HI6ML+P7L4/B6GO500W3yB7+wHedmMvjjb7+MPcNxvP6aAem1Yv2Rv3g9vvM7dxi2IOGO5hd8hy4dqT58hy4dq08HOZvwM8DBwxeCb2PpRGwq/ExRsQxOE9ft8zDTYSDpggIPs98wtjptK763E/ygz4tIwGtd4dsc2gKsT9vOpAuIR/yWh+wEZsPMxSQrIehWDIjTtolKp850uoBMsWyadFnPuq4wRhO5mn74ExMp7LBpTRSEA15sH2ivaY98ZTyJXYPtUjbD3vWd8HuZMZTkmbNz2LWm3TJ+o563XL8GYb8XH/vWYXzt2Yu499oBV8L7mu19+OcP7MV/vnsrvvhrN0tZQfVEbU5wE840v+A7WTo2XTqcc9ssfUD7hJC3CU+z2rAFtIx9r4eZtmUaOTy2gu9DwSJ8LVuwDl4DtDa/WMh8zKFIyrQTEas8HaPCd/Bm42HzeIW5jHVSpsDqtK1TD76grz3UcHhqTK/wnar0ymnbyvrzM/poQonNy+HOCMoqN1o7p1MFzGZqB5fbcdP6OF68mEBZ1f5uHh9P1gwtsSMa9GHfxi48cnQCU8k8nr8wZxlLYEZHxI+P3rMNR8eSYIzhD+7ZJr1WcM+ufnz0nm2O/42Jy0PzC37Z3ke3E3y7ebaCkM+LsspNh0TnS9bzbAFNdK0Gmcu0ZVYy8c2rdKfKLRowH4KStAlOE1QSM2vXJx2ikQUdkUBDhV9QykgXFMukTEGlwq8V/GmLWbb1rI2HMZao7aUfS+QQCXgdr1uEoFXbMmIT1e7glEDcFER+vWiTFAFnTty0vhPpgoKTkykcHkmgoKi4eYPzpqvgbXvW4vxsFu/41FMAgPv22B8+quc379qE7/3nO/DoH7zKmMRFXD00v+A7ePg+D4OHmbdlygi+2AMwq/JzJfuTsoB1Jr6wauzWi4NV9Z8QlLKKgqLadukAmkdvaunYBKcJjCEodVV6JRrZfn087MdCXZeOuAHIePgAGk7bOsUqCNbGtVz76pv0WCKHQZPRhvV4PAwbe6I4U9UPf35Gm0Vrd+hKsNM4AKUJvRg9KA5GOXHTOv0Q0/k5PH5qBowBt1RNinLivj1rsXOwHSPzObzn5mFsXoRoX7Omw7GbiVidtEyXjpWvyxjT5tqaVOjGPFsb0RWCXCiVGyrqvITghwMe5E0snbyLCr8+XkEMMLfr0gEqiZn12CVlCqyGoEhbOhG/kQEjEBW7U5eOaNusP207k5IU/M4wyirHZKpgWDhjiRzWSGy6AsDmvhheHqkM5Tg/m8FwV8T2pKugQz/kJE64Hp9Ioa8t6Pg7C4a7wtjUE8WDL45iPlPELRu7XNkjAZ8H3/zQfpycTOH6obj0OqI5aPkKH9D8fTNLxylLv/o5s08ImuDb/xFbWTpZiS4dqyEoTtOuBNGghYdfcGHpNGzaKgj6PI43OrMhKEaXjYOA+b0exCP+mtO2yXwJmWLZ8NjtEMJePW5wNJGX6rIBgC29MVyazxo35fMzWcdTstXsGY7j4Pl5cM7xwsV5XGeTY1MPYwzv378eL15M4PxsFr+6f4P0WkE06MMN6zrhpc3PlqP5K/yyNoTcZ/OXO2AxtUrKw7fptMmXVEdP2dLDd4hWBqzn2oq4BbtPB4CWlVOf6wJols6mHmc7CDCp8LP2sQqCjnAAC9naPn6Zk7KCLr0XXyDaKgclRFsI+2giC6ALBaWMmXTBVYXPudZOub2/DednM9i3Ua6XHQBu3dyN7708jidPz+LcTAa/fMs650VV/Or+DSiVVYQDPtx7rbvWRqK1aQnBD3jNh5ALtMTLRtEtOBycqn7OusKX8PAtunRCfusefqC6wq+zdIr2A8wFbUFzD1/G0vF5PYgFfY2btnk5wY9H/CiW1ZoIaFGxy9gyPdFgzaBn0fUiU+FXbBxtjbhZyAq+mCx1ZlpLqcwWy9g1KOfBA8Brd/ThzxnwK59/FgBwt0PiYz0eD8P9d212tYYggBaxdOzsHEATbfMuHd3Dt+3Dt8/DcfbwvZZ9+HYtmUD1IPNa0U0b067s11taOnlFKliqI+xvsHQWciXbHnyB2Wnb6XQBAa8Wf+xEY4Wv2TNOB6cA7c+8KxowIo1Flo3MpiugRRx4mLbhKsYDWg0AMWNtPIw369G8914zYJygJYjLTfNX+A4nZQHN319sW6bo0jGv8FVnwfd7MWZxs3DqsolaVfi6pePUlhnT8/SrIwoKShnFsupY4QOarVNv6STzJduhEoJ4VUSyqKy1PvqA1CGi7lgAz52vCP74Qh6MWY8nrGdtPGwkXIqhIiKrxgkxxenZc7OYzRQRDXgd0yrr+R/v2o237F6Du7atTC460Zq0RIXvdPLSuktHF3zbLB1vzWtr1ktu2pqdltWGnzistejDzzhMuxIIUa8OUJMZfiIwy8RfyJWkKvRKp03FlplJF6RDrXpiQcxni8aNejyRR08s6PhpTrC5N4ozepfQ2ZkM2oI+29C1em7b0oPnz8/j689dxJ1bex3/jtUT8Hlwz65+20+PBLHcNL/gl50tnYDXY/j1NWuNCt+uLVPvw1+kpROysnRkKvyg/aatU1umEaBWWJzgt4f9ppu2MpaOqMQnk7WCL3NwCtBaKzmv+O/jybyUfy/YPtCOsYW8nhiZwua+mKsUxHfvrYxofvfNwzavJIjVQ/MLvqJaxioIgn6HPnzbTVvzCl8pq1BU7ujDhy02bbNFxXGt6OCp78OXbcuMmSRmGsFpQWfRbg/5jRsEAJTKKpJ5RaqnvCL4lROvsgenAGBIt4GELTOxkJPy7wXbBzQL5uhoEkdGF3C9Cw8e0E7M/uv9t+J/vns3XrNDLjGSIFaapvfwS5IVvtlAblH122bp+MwrfHHyVrYPvz5mOFdSjY1NKzwehkigccyhiEuIOXxCECMMqyt8sYkadwgwAzRLp7rCn8+I8YTOoh0OeNEe8hmCr6ocs+miVEsmAAzp2fMjiRw45xhP5LF/k/yJ0xvXdYIx4MtPn0emWHYc02fGLS7ejyBWA01f4RckunScN20lTtrWrc9JRCMAmvCpvDGeOS/RpQNonTr1FX5aDz9zShWMmVg6C5JZOIB22jZdUIyIAnHytUfy5Gd/e8gQ/GS+BEXl0hX+QEcIHgZcnM1iJl1EqqBIhZcJ4pEArl3Tge8fmQCAFRsqTRBXkqYXfBlLJ+DzLt7SEV069RW+w7QrgXFwq24ISrak2J6yFUQCvgZLKF0oSUXemlk6CReCL14jbhiij15241UTfM3Dl5lHW03A58GGnihOTaWMiAa3uTAfepXWy/7Om4akOosI4mqn6S2dYll1FD+rTHuZLp2QhYcvbhYybZmAtknbgYrI5oqqpOB7Gw5PpQuKYdfYYVbhJyUGmAhEvMJCroR4JGB03MjmwvS3h3DmjJbNPrFQMB6TZVtfG05OpozkSbetkW+6fhB71r1WangIQTQDVOHDui3TKUsf0DLtGWus8MXYQsdN24D2s+vjFXISm7aAJvj1a2VOygJVg8xrPPwiQn7nLBygOjFTWz9jnJSVFfwgplIFqCo3Nl9l82wAYPuAFmvw2IlpdEUDrrp0BGvj4at6RilBuKE1BF+mLdPipK3Pw2xTEBljCPm8DfHIeaPCd960BWojjjnnelumnKVTX+GLASZOmM21XciVEA/LCXZ73RCU2XQBPg+THkw90BFCWeWYzRQxmsjBw+BqMPVtm7uhcuDHxyZx66YuEm6CcKDpBV+mS8cyWqHkvBbQLJ+levjVVXqxrELlzmsB8zGH6YJche/3ehD0eRq6dGT8e6ASkSziFeb0AeSyI+iEbz6ZzGN0XmurdHOA6cb1ncanr7fuXiu9jiBaleb38CUtnYKiNrRGOg0wFwR9jZ8QZGbSVj9f3dYp1spV+CaCL1nhA5qtU9+l0yHRkgk0DkGZSRelN2yBSnbN+dmMkSnvBr/Xgx/+/l144eI8Xn+NuwAygmhFmr7ClzlpK0S9VK6dDVtQylJH30P+xtOy0n34gUZLR2aerSAS9JlW+DGJg1OAHqBWL/iyFX6oztLJFByz7KvZ0heDhwEnJ1I4OZmWnutazYaeKN5x4xDZOQQhQdMLvmwfPtDYC19QVNsOHYFZhS+mWDndMMImlo7M8BNBxF978KqscmlLB9CnXjV4+HKCHwl4EfR5jP772XTRGD8oQ8jvxfruKH56YhrpgrIowScIQp6mF3zZTVvx2moKJWc7CLCq8Bfv4cvaQYBW4YvES6AShCYr+G0hX03EsRsPnzGGwY4QxvTTrjPpArqj8pYOANwwHMfLesTwDcPyw7gJgnBPUws+59wYgGJHQK/C6wU/rziHnwHmFX5W0ocXVXz1DUPk08j00otkyrQu9KJal/Xwq3PlC0oZuVJZKlZBMNgRxvhCHolsCdliGWvi7loj33T9IACtPXLnIFX4BHE5aepNW0Xl4Ny+jx6onlrV2Gnj5MEDWpVe3xrpdtO22sMXP0smwExU8qm8gvaQ3/DjZW4WgCb483p+jptYBcFgPIRnzswaoxLdbry+dkcfvvhrN2NDT5R8eIK4zDS14JfKzuFn1c83WDqK8yldQLthzGXqunQkRhQC5pZO2ki7dP50ISZTaSmX4ap4YznR7ooEMJ8toqxyLOjC3xGR9+HXxsOYSOZxdjoDABjudCf4jDFKmySIK0RTWzrGSVlJwW/YeC2pUl06QZMh6Nmi4phnDwBeD0PA5zEVfDlLp/a0q4g3dmPpcK6dsBWbr10uBH9LXwwqBx49PgUAGO6SPylLEMSVhQQfNl06kpZO0O9p2LTNSqZdApqtky+aCL6EaFcsnVLNWtlN2y69b34+W8R0Ssuz6WuX33jdMaAN7/7OoTFs6I5If7IgCOLKsyRLhzHWBeBfAWwAcB7AL3HO501edx5ACkAZgMI537uU95WlIJGFA1R5+KX6Cl9207axws8Vy1JtlUAlE1+QKSjwMLkuHSHsotPG7aat6JufSRcxJQRfMpMeqJ0Du5hMeYIgrhxLrfA/DuBRzvlWAI/q31vxGs75nisl9kClYneq8I2I4vpNW0WV3LQ1r/BlTsoCWqdOrupmk8oriAZ9UpuYIs9GePduRhQCWoAZoMUbTKXyCHg9rjZt/V4P3nXTEADgnTfRqD+CWM0sddP2PgCv1r/+EoCfAfjYEn/msiGTdglURRyb5OEs1sPPubB0QnVjDjMFBW0uohGASrzBfLYIn4dJV/iDHZrnPpbIYzpZQG9b0HW3zF+9/Tr85l2bsK2f2ioJYjWz1Aq/n3M+DgD6v63aLTiAHzLGDjLG7rf7gYyx+xljBxhjB6anp5d0cbJdOpVB5BXR5py7aMvUwtfKaiWaIVtS5Ct8vwe5UqWtM11QHOfRCoI+L8J+r9FSOZ8tIR7xS4t2NOhDe8iH8YUcxhfyRsXvhoDPQ2JPEFcBjqrCGPsxgAGTp/7UxfvczjkfY4z1AfgRY+w45/xxsxdyzj8L4LMAsHfvXm72GllkN21DJgFmisq1xEqJCj+qd+PkSmWjstYsHTnRjgZ9NcPAZQeYCLTDU5rgJ7JFxF102QBalT+WyOP8bAb7N9OcVoJoVhxVhXP+OqvnGGOTjLFBzvk4Y2wQwJTFzxjT/z3FGHsQwD4ApoK/nEhbOiaCLxtvDAARvV8+W6ikVOZdbNq2hXwYX8gb36cL8mmXgDZwfD6rtVTOZ4vodHFSFgDWdUfwylgS4wt5bOyWnwtLEMTVxVItnYcA/Kr+9a8C+I/6FzDGooyxNvE1gF8AcGSJ7ytFwaWlU71xKuwdGUtHVPjVw8SzkgNMgMYAs4xLwa+OR0hkS64r/GvWtGM0kQMAV4PACYK4uliq4P8tgHsYY6cA3KN/D8bYGsbYw/pr+gE8wRg7BOA5AN/jnP9gie8rhbSl47Ou8IOSQ0gA1MQrZF1U+LGg3+ijB7TWSlkPHwA6IwEkllDhX7e2w/h638YuV2sJgrh6WFKXDud8FsDdJo+PAXij/vVZALuX8j6LRdbS8XgYAl5PTVumyNWRGYASrfLtAS2iuKio0l06bSEt8bKscng9zLWl0xnxYy5TBOcc85kSOl1k0gPAHVt7cPuWbsTDAVdDxAmCuLqgLB0dbUyhmaXjosLXEyuz+r9lLR3RWpkpau2YbgW/KxpEMq9gKlVAsaxiwKVoB31efPU3bgXnS9ojJwhildPUgi9r6QB6vMEiN22NCr+grTGSMiW7dIS4p/IK/B4PVC6fdgkAg/rg70OXEgDgWvAFlFZJEM1Ncwt+Wc7SARqHmIiDVCGJm0Vjha9n4UtaOkLc03kFfq8mum48/EE9g/6FiwkAQH8H2TIEQTTS1IJfcGHLaPEI1ZaOiwo/ICr8OsGXtnS0TdZ0oWR8GpE9aQtUTsu+eFGLMSIfniAIM5pa8I1OG4kqPeT31mzauvLwg6LC1y0dMYRcUvDF1KpEtgS//mnETYUvpkw9e24OAa/HVfgZQRCtQ1PHIxcUFV4Pg0/G0vFZefjOawNeD3weZmzW5owKX060O/W++flsyZg+1RWVb62MBHwY6tSq/B2DbcZNgyAIopqmVoZ8qSzlwQMi077K0jHaMp2rdMYYIgEvMvqmrdsuHSH4iWwR8/oBqk6Xh6f2bdD6569Z0+5qHUEQrUNTWzoFRZU6OAVo1o0YAAK4O2kLaBaMUeG78P8BrS3T62GYzxbh0Ttlulz20r/3lnVIFxR86FWbXa0jCKJ1aHLBL0v594BZl4470Y4EvIaH73bT1uNhiIf9mM+W4GEMHlYZXSjLzRu6cPMGOiVLEIQ1TS34+ZIqLdghX32Xjva17A0jGvQtuksH0ALQEtkiGDQ7x2n4OUEQhFuaWvBdV/jV0Qolba3sYaTqCl/k4rjptKkOQHMbjUAQBCFDk2/aqtKCHw40dunIfjoAtF584eGn8trwEzfdMn3tIUws5DGxkEdvjNoqCYJYfppa8AtKWX7TVrd0RJ6Mm5sFAESCPiNaIZUvSc+UFQx1akNILs7lMNwVdrWWIAhChiYXfHnRFjcGEamQV9xW+F4jWiGVV4zTs7IMxcMollXMpAsY6oy4WksQBCFDUwu+q01bIfj6Zq3sPFtBJFBd4SuuK/y1nZWqfqiTKnyCIJafphZ8d5u2+iBzpdJaKXtSFgCiQa3C55zrlo67Cv/aNZUhJNUDSQiCIJaL5hb8kip1UhaoTL0SsQi5ovyIQkA7PKVybR7tYir8vvYQdg/Hsa4rgq39ba7WEgRByND0bZmytowxyFyv8DPFsqvZsHEjHqGEZF4xAtHc8I3/61bQDBKCIC4XzS34bip8YenoHn62qCAalK/wu3TBn8sUkcyVXJ+UBeRyewiCIBZLU1s6eaWMoNsKv7Q4D79TT7e8OJdFsayih3rpCYJYZTSt4JdVjlKZG968EyK7Xnj42YLiMhpBq/BPTaUBAD1tdFqWIIjVRdMKvgg/k63wxYSpdEHrtMmWyoi6EHxh6ZzRBb87ShU+QRCri+YV/JL8TFqgknuTKSj6iVvt9Kws7WE/GANOTqYAAN0xqvAJglhdNK/g6ydmZaMVolUVvjgx66bC93oYBttDhqVDeTgEQaw2mlbw3cyzBSrinimUjROzYRebtgCwvjsKAAj4PK4HmBAEQVxumlbwRYUvG63g83oQ8nuQKSrIltyNKBSs79YycLb1x6Tm6BIEQVxJmlaV3Fb4ABAL+oyTsoD7qVO79Hmy67oo/IwgiNVH0x68Mjx8F4eZokEf0nkFC1ltgEl72N0fz/v2rUNZ5bhza6+rdQRBEFeCJhZ8MZNWvsKPBnzIFBQk9YlVbit8n9eDD96+0dUagiCIK0UTWzruK3xh6SRzosJ3H49AEASxWmlawXd78ArQBD6ZV5DUPXy3iZcEQRCrmaYV/Lxx8MrFadmoH/N6+JnbmbQEQRCrnaZVtMVU+J3RAOayRSwsMu2SIAhiNdO0gl/x8OV/xa5IAEVFxUQy77pDhyAIYrWzJMFnjL2LMXaUMaYyxvbavO5extgJxthpxtjHl/KesuSK4vCUm4hj7XTsiYkUxRsTBNF0LLXCPwLgHQAet3oBY8wL4JMA3gBgF4D3MsZ2LfF9HckUy/B7GQIuKvxOPfFyKlXAYAcNEicIorlYkm/BOT8GAIwxu5ftA3Cac35Wf+0DAO4D8MpS3tuJbEExAtFkqU64HOwILfclEQRBrChXwsNfC+BS1fcj+mOmMMbuZ4wdYIwdmJ6eXvSbZoplRF2Gn23ujRlfD8ZJ8AmCaC4cFZEx9mMAAyZP/Snn/D8k3sOs/Lcc1c05/yyAzwLA3r17Fz3SO1t0N7EKADqqDlpRHg5BEM2Go+Bzzl+3xPcYATBc9f0QgLEl/kxHMoWyqwEmgjdeN4Dnzs3jts09l+GqCIIgVo4r0Xv4PICtjLGNAEYBvAfA+y73m2aLiqsBJoJPvPdGKCqH12O7L0EQBHHVsdS2zLczxkYA7AfwPcbYI/rjaxhjDwMA51wB8DsAHgFwDMA3OOdHl3bZzmQKZVctmQKPx11nD0EQxNXCUrt0HgTwoMnjYwDeWPX9wwAeXsp7uSVbVBANuq/wCYIgmpWmLWUzxcVV+ARBEM1K0wp+Or84D58gCKJZaUrBz5fKyJXKRlQCQRAE0aSCn9BHFMYjlHhJEAQhaErBn88WAVSycQiCIIgmF3yq8AmCICo0peAblk6YKnyCIAhBUwq+YelEqcInCIIQNKXgjyVy8HoYuqhLhyAIwqApBf/YeApbemMIuhhgThAE0ew0peAfHVvANWvaV/oyCIIgVhVNlz1QKqu4Y0sv7txK8cYEQRDVNJ3g+70e/N0v7V7pyyAIglh1NKWlQxAEQTRCgk8QBNEikOATBEG0CCT4BEEQLQIJPkEQRItAgk8QBNEikOATBEG0CCT4BEEQLQLjnK/0NVjCGJsGcGGRy3sAzCzj5awkzfK7NMvvAdDvslqh3wVYzznvNXtiVQv+UmCMHeCc713p61gOmuV3aZbfA6DfZbVCv4s9ZOkQBEG0CCT4BEEQLUIzC/5nV/oClpFm+V2a5fcA6HdZrdDvYkPTevgEQRBELc1c4RMEQRBVkOATBEG0CE0n+IyxexljJxhjpxljH1/p61kKjLEvMMamGGNHVvpalgJjbJgx9lPG2DHG2FHG2EdW+poWC2MsxBh7jjF2SP9d/nKlr2kpMMa8jLEXGWPfXelrWQqMsfOMsZcZYy8xxg6s9PUsBcZYnDH2TcbYcf3/mf3L9rObycNnjHkBnARwD4ARAM8DeC/n/JUVvbBFwhi7C0AawJc559eu9PUsFsbYIIBBzvkLjLE2AAcBvO1q/O/CGGMAopzzNGPMD+AJAB/hnD+zwpe2KBhjHwWwF0A75/zNK309i4Uxdh7AXs75VX/oijH2JQA/55x/jjEWABDhnCeW42c3W4W/D8BpzvlZznkRwAMA7lvha1o0nPPHAcyt9HUsFc75OOf8Bf3rFIBjANau7FUtDq6R1r/16/9clVUTY2wIwJsAfG6lr4XQYIy1A7gLwOcBgHNeXC6xB5pP8NcCuFT1/QiuUmFpVhhjGwDcAODZFb6URaPbIC8BmALwI8751fq7/P8A/giAusLXsRxwAD9kjB1kjN2/0hezBDYBmAbwRd1q+xxjLLpcP7zZBJ+ZPHZVVl/NCGMsBuBbAH6Pc55c6etZLJzzMud8D4AhAPsYY1ed3cYYezOAKc75wZW+lmXids75jQDeAODDuh16NeIDcCOAT3HObwCQAbBse5HNJvgjAIarvh8CMLZC10JUofvd3wLwVc75t1f6epYD/aP2zwDcu7JXsihuB/BW3ft+AMBrGWNfWdlLWjyc8zH931MAHoRm716NjAAYqfrU+E1oN4BlodkE/3kAWxljG/XNjvcAeGiFr6nl0Tc6Pw/gGOf871f6epYCY6yXMRbXvw4DeB2A4yt6UYuAc/7HnPMhzvkGaP+f/IRz/isrfFmLgjEW1ZsBoNsfvwDgquxs45xPALjEGNuuP3Q3gGVrbvAt1w9aDXDOFcbY7wB4BIAXwBc450dX+LIWDWPs6wBeDaCHMTYC4M85559f2ataFLcDeD+Al3XvGwD+hHP+8Mpd0qIZBPAlvSPMA+AbnPOruqWxCegH8KBWV8AH4Guc8x+s7CUtid8F8FW9aD0L4IPL9YObqi2TIAiCsKbZLB2CIAjCAhJ8giCIFoEEnyAIokUgwScIgmgRSPAJgiBaBBJ8giCIFoEEnyAIokX4PwubE5w8joqeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,si(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8facc6b7",
   "metadata": {},
   "source": [
    "## 4.数值微分"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc6ff99a",
   "metadata": {},
   "source": [
    "### 4.1前向差分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0e6385c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([120.        , -54.5105937 , -59.07148423, 102.97463947,\n",
       "       -40.07617216, -56.77630057,  87.82924433, -28.39720199,\n",
       "       -53.67955341,  74.44906819, -19.04676881, -50.065159  ,\n",
       "        62.70568862, -11.65133549, -46.15617939,  52.46371037,\n",
       "        -5.88609501, -42.12510844,  43.58590267,  -1.47032921,\n",
       "       -38.10273562,  35.93705021,   1.83711382, -34.18573823,\n",
       "        29.38675642,   4.24214341, -30.44314481,  23.81140171,\n",
       "         5.91949613, -26.92180345])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 解析结果\n",
    "t = np.arange(0,3,0.1)\n",
    "di(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a9cd2303",
   "metadata": {},
   "outputs": [],
   "source": [
    "## 定义前项差分\n",
    "## 尽量减小h的值,使误差在1左右\n",
    "def qian(t):\n",
    "    h = 1e-6\n",
    "    return (j(t+h)-j(t))/h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cb71d08b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([119.99974   , -54.66906279, -58.92732012, 102.98709181,\n",
       "       -40.21792703, -56.65881969,  87.85080795, -28.52308815,\n",
       "       -53.58472943,  74.47685124, -19.15780292, -49.98945188,\n",
       "        62.73739578, -11.74863602, -46.09649646,  52.49754478,\n",
       "        -5.9708283 , -42.07876443,  43.62048078,  -1.54366842,\n",
       "       -38.06741319,  35.97132882,   1.77401935, -34.15944954,\n",
       "        29.41997005,   4.18819027, -30.42419507,  23.84300949,\n",
       "         5.87364205, -26.90875659])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qian (t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca71ee23",
   "metadata": {},
   "source": [
    "### 4.2后项差分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0da785f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "## 定义后向差分\n",
    "## 尽量减小h的值,使误差在1左右\n",
    "def hou(t):\n",
    "    h = 1e-6\n",
    "    return (j(t)-j(t-h))/h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "29eea0b7",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([119.99986   , -54.3519428 , -59.21545153, 102.96184387,\n",
       "       -39.93428361, -56.89359227,  87.80738795, -28.27122109,\n",
       "       -53.77419852,  74.42103696, -18.93567113, -50.14069927,\n",
       "        62.67377241, -11.55399607, -46.2157085 ,  52.42970107,\n",
       "        -5.80134204, -42.17131205,  43.55117924,  -1.39698505,\n",
       "       -38.13793107,  35.90265177,   1.9002022 , -34.211913  ,\n",
       "        29.35344481,   4.29608244, -30.46199311,  23.77971455,\n",
       "         5.96533051, -26.93476058])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hou(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da0be7c8",
   "metadata": {},
   "source": [
    "### 4.3中心差分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "31a5eec0",
   "metadata": {},
   "outputs": [],
   "source": [
    "## 定义中心差分\n",
    "## 尽量减小h的值,使误差在1左右\n",
    "def zhong(t):\n",
    "    h = 1e-5\n",
    "    return (j(t+h)-j(t-h))/(2*h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "0e9b466c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([119.980001  , -54.50150377, -59.06164427, 102.95747747,\n",
       "       -40.0694884 , -56.76684224,  87.81460613, -28.39246516,\n",
       "       -53.67061042,  74.4366597 , -19.0435908 , -50.05681774,\n",
       "        62.69523713, -11.64939046, -46.14848906,  52.45496572,\n",
       "        -5.88511122, -42.11808948,  43.57863756,  -1.47008173,\n",
       "       -38.09638666,  35.93105985,   1.83680975, -34.18004177,\n",
       "        29.38185776,   4.24143822, -30.43807184,  23.80743229,\n",
       "         5.91851112, -26.91731714])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zhong(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb70259c",
   "metadata": {},
   "source": [
    "## 5.数值积分"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aacdbf33",
   "metadata": {},
   "source": [
    "### 5.1梯形积分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "71f12a58",
   "metadata": {},
   "outputs": [],
   "source": [
    "##用梯形来近似某个曲间上的定积分\n",
    "def ti(a,b):\n",
    "    S = 0\n",
    "    p = (b-a)/100000\n",
    "    for i in range(0,100000):\n",
    "        S=S + p*(j(a+i*p)+j(a+(i+1)*p))/2\n",
    "    return S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8c26293d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0091050895748037e-05"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 用原函数来求定积分\n",
    "si(3)-si(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "51e27c82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0083481917445138e-05"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 用梯形积分来求定积分\n",
    "ti(0,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "523103f7",
   "metadata": {},
   "source": [
    "### 5.2辛普森积分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "90110d45",
   "metadata": {},
   "outputs": [],
   "source": [
    "def xin(a,b):\n",
    "    S = 0\n",
    "    p = (b-a)/10000\n",
    "    for i in range(0,10000):\n",
    "        S=S + p*(j(a+i*p)+j(a+(i+1)*p)+4*j((a+i*p+a+(i+1)*p)/2))/6\n",
    "    return S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "04d00efc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.009396651473909e-05"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xin(0,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b13ea0b",
   "metadata": {},
   "source": [
    "### 5.3龙贝格积分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "585e7ccc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "积分结果为：0.0000106474\n"
     ]
    }
   ],
   "source": [
    "#  龙贝格法求积分(来源CSDN)\n",
    "import math\n",
    "a=0             # 积分下限\n",
    "b=3            # 积分上限\n",
    "eps=1e-5     # 精度\n",
    "T=[]            # 复化梯形序列\n",
    "S=[]            # Simpson序列\n",
    "C=[]            # Cotes序列\n",
    "R=[]            # Romberg序列\n",
    "def func(x):    # 被积函数\n",
    "    ## y=math.exp(-x)\n",
    "    return 2*E*np.sin(d*x/(2*L))*np.exp(- 0.1 *x/(2*L))*(1/d)\n",
    "def Romberg(a,b,eps,func):\n",
    "    h = b - a\n",
    "    T.append(h * (func(a) + func(b)) / 2)\n",
    "    ep=eps+1\n",
    "    m=0\n",
    "    while(ep>=eps):\n",
    "        m=m+1\n",
    "        t=0\n",
    "        for i in range(2**(m-1)-1):\n",
    "            t=t+func(a+(2*(i+1)-1)*h/2**m)*h/2**m\n",
    "        t=t+T[-1]/2\n",
    "        T.append(t)\n",
    "        if m>=1:\n",
    "            S.append((4**m*T[-1]-T[-2])/(4**m-1))\n",
    "        if m>=2:\n",
    "            C.append((4**m*S[-1]-S[-2])/(4**m-1))\n",
    "        if m>=3:\n",
    "            R.append((4**m*C[-1]-C[-2])/(4**m-1))\n",
    "        if m>4:\n",
    "            ep=abs(10*(R[-1]-R[-2]))\n",
    "Romberg(a,b,eps,func)\n",
    "# print(T)\n",
    "# print(S)\n",
    "# print(C)\n",
    "# print(R)\n",
    "# 计算机参考值0.6321205588\n",
    "print(\"积分结果为：{:.10f}\".format(R[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "babe2003",
   "metadata": {},
   "source": [
    "### 5.4 高斯积分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7a266f07",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(p):\n",
    "    return 2*E*np.sin(d*p/(2*L))*np.exp(-(0.1)*p/(2*L))*(1/d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "fea6f7c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10000\n",
    "tiList,CiList = np.polynomial.legendre.leggauss(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "15cb5ca2",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 0\n",
    "b = 3\n",
    "xiList = (b-a)/2 *(tiList-1)+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "bee830f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0091050894124326e-05"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(b-a)/2 *CiList.dot(f(xiList))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8303182",
   "metadata": {},
   "source": [
    "## 6.分享经验"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81d15328",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e4ccae7c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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